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Strong convergence theorems for relatively nonexpansive mappings in a Banach space

✍ Scribed by Xiaolong Qin; Yongfu Su

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
210 KB
Volume
67
Category
Article
ISSN
0362-546X

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πŸ“œ SIMILAR VOLUMES

On Reich’s strong convergence theorem fo
On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces
✍ S.S. Chang; H.W. Joseph Lee; Chi Kin Chan πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 185 KB

The purpose of this paper is to study Reich's strongly convergence theorems for asymptotically nonexpansive mappings in Banach spaces. Under some general conditions an affirmative partial answer to Reich's open question is given and some recent results are improved and generalized.

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In an infinite-dimensional Hilbert space, the normal Mann's iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann's iterative process for an infinite family of nonexpansive mappings in the fra